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Hardware-Efficient Quantum Optimization Layered Algorithms and Experiments

Quantum optimization algorithms, such as QAOA, that implement parametrized stochastic optimization solvers attempt to identify low-energy solutions of Ising systems by exploiting available quantum effects in noisy-intermediate scale machines. Engineering a well-performing parametrized quantum optimization circuit is indeed an exercise in balancing the trade-off between expressivity and implementation complexity. We show that, for MaxCut QAOA circuits defined on native hardware topology (Rigetti’s Aspen Quantum Processors), error-mitigation techniques recover simulated features of the noiseless theory. Moreover, we explore a design space for QAOA-like ansatze that perform well in theory as well as in hardware for fully-connected problems. We also discuss how efficient coherence and entanglement detection methods that could be coupled with quantum optimization experiments require only linear overhead in benchmarking time.

quantum computing↗
DOE OSTI2024

Dynamic Cooling on Contemporary Quantum Computers

We study the problem of dynamic cooling whereby a target qubit is cooled at the expense of heating up N − 1 further identical qubits by means of a global unitary operation. A standard back-of-the-envelope high-temperature estimate establishes that the target qubit temperature can be dynamically cooled by at most a factor of 1 / N . Here we provide the exact expression for the minimum temperature to which the target qubit can be cooled and reveal that there is a crossover from the high initial temperature regime, where the scaling is 1 / N , to a low initial temperature regime, where a much faster scaling of 1 / N occurs. This slow, 1 / N scaling, which was relevant for early high-temperature NMR quantum computers, is the reason dynamic cooling was dismissed as ineffectual around 20 years ago; the fact that current low-temperature quantum computers fall in the fast, 1 / N scaling regime, reinstates the appeal of dynamic cooling today. We further show that the associated work cost of cooling is exponentially more advantageous in the low-temperature regime. We discuss the implementation of dynamic cooling in terms of quantum circuits and examine the effects of hardware noise. We successfully demonstrate dynamic cooling in a three-qubit system on a real quantum processor. Since the circuit size grows quickly with N , scaling dynamic cooling to larger systems on noisy devices poses a challenge. We therefore propose a suboptimal cooling algorithm, whereby relinquishing a small amount of cooling capability results in a drastically reduced circuit complexity, greatly facilitating the implementation of dynamic cooling on near-future quantum computers. Published by the American Physical Society2024

Physics↗
DOE OSTI2022

Model predictive control for robust quantum state preparation

A critical engineering challenge in quantum technology is the accurate control of quantum dynamics. Model-based methods for optimal control have been shown to be highly effective when theory and experiment closely match. Consequently, realizing high-fidelity quantum processes with model-based control requires careful device characterization. In quantum processors based on cold atoms, the Hamiltonian can be well-characterized. For superconducting qubits operating at milli-Kelvin temperatures, the Hamiltonian is not as well-characterized. Unaccounted for physics (i.e., mode discrepancy), coherent disturbances, and increased noise compromise traditional model-based control. This work introduces model predictive control (MPC) for quantum control applications. MPC is a closed-loop optimization framework that (i) inherits a natural degree of disturbance rejection by incorporating measurement feedback, (ii) utilizes finite-horizon model-based optimizations to control complex multi-input, multi-output dynamical systems under state and input constraints, and (iii) is flexible enough to develop synergistically alongside other modern control strategies. We show how MPC can be used to generate practical optimized control sequences in representative examples of quantum state preparation. Specifically, we demonstrate for a qubit, a weakly-anharmonic qubit, and a system undergoing crosstalk, that MPC can realize successful model-based control even when the model is inadequate. These examples showcase why MPC is an important addition to the quantum engineering control suite.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

Broadband bandpass Purcell filter for circuit quantum electrodynamics

In circuit quantum electrodynamics, qubits are typically measured using dispersively coupled readout resonators. Coupling between each readout resonator and its electrical environment, however, reduces the qubit lifetime via the Purcell effect. Inserting a Purcell filter counters this effect while maintaining high readout fidelity but reduces measurement bandwidth and, thus, limits multiplexing readout capacity. In this Letter, we develop and implement a multi-stage bandpass Purcell filter that yields better qubit protection while simultaneously increasing measurement bandwidth and multiplexed capacity. Here, we report on the experimental performance of our transmission-line-based implementation of this approach, a flexible design that can easily be integrated with current scaled-up, long coherence time superconducting quantum processors.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

Qubit Assignment Using Time Reversal

As quantum computers with large numbers of qubits become increasingly available, experiments executed on a given device may not utilize all available qubits. In this case, the outcome of executing a quantum program will depend on the ability to efficiently select a subset of high-performing physical qubits. For any given quantum program and device there are many ways to assign physical qubits for execution of the program, and assignments will differ in performance due to the variability in quality across qubits and entangling operations on a single device. Evaluating the performance of each assignment using fidelity estimation introduces significant experimental overhead and will be infeasible for many applications, while relying on standard device benchmarks provides incomplete information about the performance of any specific program. Furthermore, the number of possible assignments grows combinatorially in the number of qubits on the device and in the program, motivating the use of heuristic optimization techniques. We demonstrate a practical solution to the problem of qubit assignment by using simulated annealing with a cost function based on the Loschmidt echo, a diagnostic that measures the reversibility of a quantum process. We provide theoretical justification for this choice of cost function by demonstrating that the optimal qubit assignment coincides with the optimal qubit assignment based on state fidelity in the weak error limit, and we provide experimental justification using diagnostics performed on Google’s superconducting qubit devices. We then establish the performance of simulated annealing for qubit assignment using classical simulations of noisy devices as well as optimization experiments performed on a quantum processor. Our results demonstrate that the use of Loschmidt echoes and simulated annealing provides a scalable and flexible approach to optimizing qubit assignment on near-term hardware.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

Completely Positive Map for Noisy Driven Quantum Systems Derived by Keldysh Expansion

Accurate modeling of decoherence errors in quantum processors is crucial for analyzing and improving gate fidelities. To increase the accuracy beyond that of the Lindblad dynamical map, several generalizations have been proposed, and the exploration of simpler and more systematic frameworks is still ongoing. In this paper, we introduce a decoherence model based on the Keldysh formalism. This formalism allows us to include non-periodic drives and correlated quantum noise in our model. In addition to its wide range of applications, our method is also numerically simple, and yields a CPTP map. These features allow us to integrate the Keldysh map with quantum-optimal-control techniques. We demonstrate that this strategy generates pulses that mitigate correlated quantum noise in qubit state-transfer and gate operations.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2026

Demonstration of Cross-Resonance Gates with Resonator-Assisted ZZ Cancellation

We present the characterization of a CNOT gate realized by combining cross-resonance interaction with resonator-assisted ZZ cancellation in fixed-frequency transmons on a Rigetti–SQMS co-developed quantum processor. Extending earlier work on dynamical ZZ cancellation via off-resonant resonator drives [1], we demonstrate a direct CNOT gate implementation achieved through two microwave drives on the transmons that generate a CX rotation in the |10⟩−|11⟩ subspace while selectively darkening the |00⟩−|01⟩ transition. This tunable-coupler-free approach enables high-fidelity gates and enhances the scalability of superconducting quantum architectures. [1] Z. Huang et al., Phys. Rev. Applied 22, 034007 (2024)

Heidler, Paul [Fermilab]↗
DOE OSTI2024

Observing Quantum Measurement Collapse as a Learnability Phase Transition

During a quantum measurement, superpositions of states with different observable properties probabilistically collapse into one with a sharp value of the measured observable. In macroscopic quantum systems, this collapse arises via a continuous measurement-induced phase transition (MIPT) at a critical value of the strength of interaction with the measurement apparatus. MIPTs lie outside established paradigms for equilibrium or nonequilibrium critical phenomena and delineate distinct, stable dynamical and computational phases of matter. Quantum computers enable programmable simulation of the interaction of a measurement apparatus with a dynamical quantum system, to explore MIPT phenomena over a range of system sizes while retaining quantum coherence. Yet, existing experimental protocols rely on fundamentally nonscalable postselection techniques or direct classical simulation of quantum circuits. Here, we report the scalable observation of finite-size scaling evidence for an observable-sharpening MIPT in monitored quantum circuits in a chain of Yb + 171 ions in Quantinuum’s H1-1 trapped-ion quantum processor. By leveraging an equivalent description as a statistical physics problem, we implement scalable classical algorithms to infer the value of the measured observable from a single experimental shot. This technique enables a truly scalable protocol to observe observable-sharpening MIPTs in generic classes of circuits that cannot be directly classically simulated and also provides enhanced means to detect and suppress errors in the quantum simulation. Published by the American Physical Society 2024

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2022

Error rate reduction of single-qubit gates via noise-aware decomposition into native gates

In the current era of Noisy Intermediate-Scale Quantum (NISQ) technology, the practical use of quantum computers remains inhibited by our inability to aptly decouple qubits from their environment to mitigate computational errors. In this paper, we introduce an approach by which knowledge of a qubit’s initial quantum state and the standard parameters describing its decoherence can be leveraged to mitigate the noise present during the execution of a single-qubit gate. We benchmark our protocol using cloud-based access to IBM quantum processors. On ibmq_rome, we demonstrate a reduction of the single-qubit error rate by 38%, from $1.6 \times 10 ^{-3}$ to $1.0 \times 10 ^{-3}$ , provided the initial state of the input qubit is known. On ibmq_bogota, we prove that our protocol will never decrease gate fidelity, provided the system’s T 1 and T 2 times have not drifted above 100 times their assumed values. The protocol can be used to reduce quantum state preparation errors, as well as to improve the fidelity of quantum circuits for which some knowledge of the qubits’ intermediate states can be inferred. This paper presents a pathway to using information about noise levels and quantum state distributions to significantly reduce error rates associated with quantum gates via optimized decomposition into native hardware gates.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

Digital quantum simulation of Floquet symmetry-protected topological phases

Quantum many-body systems away from equilibrium host a rich variety of exotic phenomena that are forbidden by equilibrium thermodynamics. A prominent example is that of discrete time crystals, in which time-translational symmetry is spontaneously broken in periodically driven systems. Pioneering experiments have observed signatures of time crystalline phases with trapped ions, solid-state spin systems, ultracold atoms and superconducting qubits. Here we report the observation of a distinct type of non-equilibrium state of matter, Floquet symmetry-protected topological phases, which are implemented through digital quantum simulation with an array of programmable superconducting qubits. We observe robust long-lived temporal correlations and subharmonic temporal response for the edge spins over up to 40 driving cycles using a circuit of depth exceeding 240 and acting on 26 qubits. We demonstrate that the subharmonic response is independent of the initial state, and experimentally map out a phase boundary between the Floquet symmetry-protected topological and thermal phases. Our results establish a versatile digital simulation approach to exploring exotic non-equilibrium phases of matter with current noisy intermediate-scale quantum processors.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2026

Realization of two-dimensional discrete time crystals with anisotropic Heisenberg coupling

A discrete time crystal (DTC) is an out-of-equilibrium phase of matter that spontaneously breaks discrete time-translation symmetry. Previous studies have been limited to a set of models with Ising-like couplings - and mostly only in one dimension - thus precluding our understanding of the existence (or not) of DTCs in models with more realistic interactions. In this work, by combining the latest generation of IBM quantum processors with state-of-the-art tensor network methods, we demonstrate the existence of a DTC in a two-dimensional system governed by anisotropic Heisenberg interactions. We uncover a rich phase diagram encompassing spin-glass, ergodic, and time-crystalline phases, and identify the interplay of initialization, interaction anisotropy, and driving protocols in stabilizing the DTC phase. By extending the study of Floquet matter beyond simplified models, we lay the groundwork for exploring how driven systems bridge the gap between quantum coherence and emergent non-equilibrium thermodynamics.

Phase transitions and critical phenomena↗
DOE OSTI2021

Radio frequency mixing modules for superconducting qubit room temperature control systems

As the number of qubits in nascent quantum processing units increases, the connectorized RF (radio frequency) analog circuits used in first generation experiments become exceedingly complex. The physical size, cost, and electrical failure rate all become limiting factors in the extensibility of control systems. We have developed a series of compact RF mixing boards to address this challenge by integrating I/Q quadrature mixing, intermediate frequency/LO (local oscillator)/RF power level adjustments, and direct current bias fine tuning on a 40 × 80 mm 2 four-layer printed circuit board with electromagnetic interference shielding. The RF mixing module is designed to work with RF and LO frequencies between 2.5 and 8.5 GHz. The typical image rejection and adjacent channel isolation are measured to be ~27 dBc and ~50 dB. By scanning the drive phase in a loopback test, the module short-term amplitude and phase linearity are typically measured to be 5 ×10 -4 (V pp /V mean ) and 1 ×10 -3 radian (pk-pk). The operation of the RF mixing board was validated by integrating it into the room temperature control system of a superconducting quantum processor and executing randomized benchmarking characterization of single and two qubit gates. We measured a single-qubit process infidelity of 9.3(3) × 10 -4 and a two-qubit process infidelity of 2.7(1) × 10 -2 .

47 OTHER INSTRUMENTATION↗
DOE OSTI2022

Mitiq: A software package for error mitigation on noisy quantum computers

We introduce Mitiq, a Python package for error mitigation on noisy quantum computers. Error mitigation techniques can reduce the impact of noise on near-term quantum computers with minimal overhead in quantum resources by relying on a mixture of quantum sampling and classical post-processing techniques. Mitiq is an extensible toolkit of different error mitigation methods, including zero-noise extrapolation, probabilistic error cancellation, and Clifford data regression. The library is designed to be compatible with generic backends and interfaces with different quantum software frameworks. We describe Mitiq using code snippets to demonstrate usage and discuss features and contribution guidelines. We present several examples demonstrating error mitigation on IBM and Rigetti superconducting quantum processors as well as on noisy simulators.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Parametrized process characterization with reduced resource requirements

Quantum process tomography (QPT) is a powerful tool to characterize quantum operations, but it requires considerable resources, making it impractical for more than two-qubit systems. This study proposes an alternative approach that requires significantly fewer resources for unitary process characterization with a built-in method for state preparation and measurement error mitigation. By measuring the quantum process as rotated through the X and Y axes on the Bloch sphere, we can acquire enough information to reconstruct the quantum process matrix χ and measure its fidelity. We test the algorithm's performance against standard QPT using simulated and physical experiments on several IBM quantum processors and compare the resulting process matrices. We demonstrate with numerical experiments that the method can improve gate fidelity via a noise reduction in the imaginary part of the process matrix, along with a stark decrease in the number of experiments needed to perform the characterization.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

Dynamical topological phase realized in a trapped-ion quantum simulator

Nascent platforms for programmable quantum simulation offer unprecedented access to new regimes of far-from-equilibrium quantum many-body dynamics in almost isolated systems. Here achieving precise control over quantum many-body entanglement is an essential task for quantum sensing and computation. Extensive theoretical work indicates that these capabilities can enable dynamical phases and critical phenomena that show topologically robust methods to create, protect and manipulate quantum entanglement that self-correct against large classes of errors. However, so far, experimental realizations have been confined to classical (non-entangled) symmetry-breaking orders. In this work, we demonstrate an emergent dynamical symmetry-protected topological phase, in a quasiperiodically driven array of ten 171 Yb + hyperfine qubits in Quantinuum’s System Model H1 trapped-ion quantum processor. This phase shows edge qubits that are dynamically protected from control errors, cross-talk and stray fields. Crucially, this edge protection relies purely on emergent dynamical symmetries that are absolutely stable to generic coherent perturbations. Here, this property is special to quasiperiodically driven systems: as we demonstrate, the analogous edge states of a periodically driven qubit array are vulnerable to symmetry-breaking errors and quickly decohere. Our work paves the way for implementation of more complex dynamical topological orders that would enable error-resilient manipulation of quantum information.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2025

Toward Mixed Analog-Digital Quantum Signal Processing: Quantum AD/DA Conversion and the Fourier Transform

Signal processing stands as a pillar of classical computation and modern information technology, applicable to both analog and digital signals. Recently, advancements in quantum information science have suggested that quantum signal processing (QSP) can enable more powerful signal processing capabilities. However, the developments in QSP have primarily leveraged digital quantum resources, such as discrete-variable (DV) systems like qubits, rather than analog quantum resources, such as continuous-variable (CV) systems like quantum oscillators. Consequently, there remains a gap in understanding how signal processing can be performed on hybrid CV-DV quantum computers. Here we address this gap by developing a new paradigm of mixed analog-digital QSP. We demonstrate the utility of this paradigm by showcasing how it naturally enables analog-digital conversion of quantum signals—specifically, the transfer of states between DV and CV quantum systems. We then show that such quantum analog-digital conversion enables new implementations of quantum algorithms on CV-DV hardware. This is exemplified by realizing the quantum Fourier transform of a state encoded on qubits via the free-evolution of a quantum oscillator, albeit with a runtime exponential in the number of qubits due to information theoretic arguments. Collectively, this work marks a significant step forward in hybrid CV-DV quantum computation, providing a foundation for scalable analog-digital signal processing on quantum processors.

42 ENGINEERING↗
DOE OSTI2026

Evaluating the Limits of QAOA Parameter Transfer at High-Rounds on Sparse Ising Models With Geometrically Local Cubic Terms

The emergent practical applicability of the Quantum Approximate Optimization Algorithm (QAOA) for approximate combinatorial optimization is a subject of considerable interest. One of the primary limitations of QAOA is the task of finding a set of good parameters, which is usually done using a variational optimization loop. Parameter transfer, or parameter concentration, is a phenomenon where QAOA angles trained on problem instances that are self-similar tend to perform well for other problem instances from that similar class. This suggests a potentially highly efficient and scalable non-variational learning method for QAOA angle finding. In this work, we systematically study QAOA parameter transferability from small problem sizes (16 and 27 decision variables) onto large problem instances (up to 156 qubits) for heavy-hex graph Ising models with geometrically local higher order terms using the Julia based QAOA simulation tool \texttt{JuliQAOA} to perform classical angle finding for up to $49$ QAOA layers ($p$). Parameter transfer of the fixed angles is validated using a combination of full statevector, Projected Entangled Pair States (PEPS), Matrix Product State (MPS), and LOWESA numerical simulations. We find that the QAOA parameter transfer from single instances applied to other (unseen) problem instances does not in general provide monotonically improving performance as a function of $p$ - there are many cases where the performance temporarily decreases as a function of $p$ - but despite this the transferred angles have a general trend of improved expectation value as the QAOA depth increases, in many cases converging close to the true ground-state energy of the $100+$ qubit instances. We also sample the hardware-compatible Ising models using the ensemble of transfer-learned QAOA parameters on several superconducting qubit IBM Quantum processors with 127, 133, and 156 qubits. We find continuous solution quality improvement of the hardware-compatible QAOA circuits run on the IBM NISQ processors up to $p=5$ on \texttt{ibm\_fez}, up to $p=9$ on \texttt{ibm\_torino}, and up to $p=10$ on \texttt{ibm\_pittsburgh}.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2025

On-chip pulse shaping of entangled photons

The miniaturization of optical systems via integrated photonics is critical to the ultimate scalability and performance of photonic quantum processors, yet many longstanding optical signal processing capabilities—such as Fourier-transform pulse shaping—remain unrealized on chip. In this work, we demonstrate on-chip spectral shaping of entangled photons using a multichannel microring-resonator-based silicon photonic pulse shaper. Achieving line-by-line phase control on a 3 GHz grid for two frequency-bin-entangled qudits, the pulse shaper's fine spectral resolution enables control of nanosecond-scale temporal features, which are observed by direct coincidence detection of biphoton correlation functions that show excellent agreement with theory. This work marks a demonstration of biphoton pulse shaping using an integrated spectral shaper and holds significant promise for applications in photonic quantum information processing.

Entanglement manipulation↗